Rotary abrasive tools particularly designed for cleaning or finishing interior cylindrical surfaces may be used in many settings. If a side of a filament instead of the tip can be properly positioned against the surface to be honed or finished, it has been found more work per unit time can be achieved. This is especially true when the filament has a flat side facing the direction of rotation. This positioning is advantageous in finishing and cleaning the interior of the cylinder and also at the edges of a structure. A flexible abrasive rotary tool is disclosed in copending application entitled "Flexible Abrasive Grinding Tool", Ser. No. 216,709, filed Jun. 8, 1988. The present invention relates to certain improvements in the type of tool disclosed in such copending application relating to smaller and more economical tools utilizing flat sided and other shaped monofilaments.